Duration, Yield, and Interest Rate Risk
Bonds are contracts where the issuer promises to pay periodic coupons and return the principal (face value) at maturity. The price of a bond and its yield move inversely: when market interest rates rise, existing bonds (with lower coupons) become less attractive, and their prices fall. When rates fall, bond prices rise. Duration is the primary measure of a bond's sensitivity to interest rate changes. Modified duration: for a 1% increase in interest rates, a bond with modified duration of 5 years will lose approximately 5% in price. A bond with duration of 10 years will lose approximately 10%. Duration = weighted average time to receive the bond's cash flows, weighted by present value. For a zero-coupon bond, duration equals its maturity. For coupon bonds, duration is less than maturity because some cash flows arrive earlier (coupon payments). Longer maturities = higher duration = more interest rate sensitivity = more price risk. This is the fundamental trade-off in fixed income: longer-duration bonds offer higher yields (normally) but more price volatility. The term premium compensates for this duration risk. Convexity: the price-duration relationship is not linear — it curves (convex) so that price increases from rate decreases are slightly larger than price decreases from equal rate increases. High convexity is favorable — it provides asymmetric upside.